A sequence \(\{x_n\}\) satisfies the recurrent relation below:

\[\large \begin{cases} x_0 =1 \\ x_n = -\dfrac{225}{n} (x_0 +x_1 +x_2 + ... +x_{n-1}) & \text{for } n \ge 1 \end{cases} \]

Find the value of \(x_0 +2x_1 +2^2 x_2 +2^3 x_3 + ... +2^{225} x_{225}\).

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